-2x^2+2x+5=-x^2-x-(1-x^2)

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Solution for -2x^2+2x+5=-x^2-x-(1-x^2) equation:


Simplifying
-2x2 + 2x + 5 = -1x2 + -1x + -1(1 + -1x2)

Reorder the terms:
5 + 2x + -2x2 = -1x2 + -1x + -1(1 + -1x2)
5 + 2x + -2x2 = -1x2 + -1x + (1 * -1 + -1x2 * -1)
5 + 2x + -2x2 = -1x2 + -1x + (-1 + 1x2)

Reorder the terms:
5 + 2x + -2x2 = -1 + -1x + -1x2 + 1x2

Combine like terms: -1x2 + 1x2 = 0
5 + 2x + -2x2 = -1 + -1x + 0
5 + 2x + -2x2 = -1 + -1x

Solving
5 + 2x + -2x2 = -1 + -1x

Solving for variable 'x'.

Reorder the terms:
5 + 1 + 2x + x + -2x2 = -1 + -1x + 1 + x

Combine like terms: 5 + 1 = 6
6 + 2x + x + -2x2 = -1 + -1x + 1 + x

Combine like terms: 2x + x = 3x
6 + 3x + -2x2 = -1 + -1x + 1 + x

Reorder the terms:
6 + 3x + -2x2 = -1 + 1 + -1x + x

Combine like terms: -1 + 1 = 0
6 + 3x + -2x2 = 0 + -1x + x
6 + 3x + -2x2 = -1x + x

Combine like terms: -1x + x = 0
6 + 3x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-3 + -1.5x + x2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -1.5x + 3 + x2 = 0 + 3

Reorder the terms:
-3 + 3 + -1.5x + x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1.5x + x2 = 0 + 3
-1.5x + x2 = 0 + 3

Combine like terms: 0 + 3 = 3
-1.5x + x2 = 3

The x term is -1.5x.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5x + 0.5625 + x2 = 3 + 0.5625

Reorder the terms:
0.5625 + -1.5x + x2 = 3 + 0.5625

Combine like terms: 3 + 0.5625 = 3.5625
0.5625 + -1.5x + x2 = 3.5625

Factor a perfect square on the left side:
(x + -0.75)(x + -0.75) = 3.5625

Calculate the square root of the right side: 1.887458609

Break this problem into two subproblems by setting 
(x + -0.75) equal to 1.887458609 and -1.887458609.

Subproblem 1

x + -0.75 = 1.887458609 Simplifying x + -0.75 = 1.887458609 Reorder the terms: -0.75 + x = 1.887458609 Solving -0.75 + x = 1.887458609 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 1.887458609 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 1.887458609 + 0.75 x = 1.887458609 + 0.75 Combine like terms: 1.887458609 + 0.75 = 2.637458609 x = 2.637458609 Simplifying x = 2.637458609

Subproblem 2

x + -0.75 = -1.887458609 Simplifying x + -0.75 = -1.887458609 Reorder the terms: -0.75 + x = -1.887458609 Solving -0.75 + x = -1.887458609 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -1.887458609 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -1.887458609 + 0.75 x = -1.887458609 + 0.75 Combine like terms: -1.887458609 + 0.75 = -1.137458609 x = -1.137458609 Simplifying x = -1.137458609

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.637458609, -1.137458609}

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